Estimate the solution to the system of these linear equations based on the graph.y=−x+6 y=3x−2
Based on the graph of the two linear equations, it appears that the lines intersect at a point that is roughly (2, 4). Therefore, the estimate for the solution to the system of linear equations is x ≈ 2 and y ≈ 4.
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Apologies for the confusion. Based on the graph, it appears that the lines intersect at a precise point, which is (2, 4). Therefore, the solution to the system of linear equations is x = 2 and y = 4.
To estimate the solution to a system of linear equations based on the graph, you can look at the point where the two lines intersect. This intersection point represents the solution to the system.
Let's start by finding the intersection point of the two lines.
The first equation is y = -x + 6, and the second equation is y = 3x - 2.
To find the intersection point, we can set the two equations equal to each other:
-x + 6 = 3x - 2
Now, let's solve this equation for x.
First, we can add x to both sides to simplify:
6 = 4x - 2
Next, let's add 2 to both sides:
8 = 4x
Finally, divide both sides by 4:
x = 2
Now that we have the x-coordinate of the intersection point, we can substitute it back into one of the original equations to find the y-coordinate.
Let's use the first equation y = -x + 6:
y = -(2) + 6
y = -2 + 6
y = 4
So, the solution to the system of linear equations is (2, 4).
Based on the graph, the intersection point appears to be at coordinates (2, 4). Keep in mind that this is an estimation, as we are reading the coordinates from the graph.